Along with the Grassmannian, there is a TQFT: \(U(k-J)^{\mathcal {N}=1}_{-\frac{k-J+2}{2},-1}=U(k-J)^{\mathcal {N}=0}_{-1,-1}\) . This topological quantum field theory is almost trivial since it has only one transparent line, which has spin \(\frac{1}{2}\)  (see [1]}). In particular this model has \(WI=1\) . The presence of the non-trivial TQFT is a problem for the proposal (REF ), since in \(4d\)  we have a Wess-Zumino model.
